We report on recent progress in developing diffraction gratings which can potentially provide extremely high spectral resolution of 10[superscript 5]-10[superscript 6] in the EUV and soft x-ray photon energy ranges. Such a grating was fabricated by deposition of a multilayer on a substrate which consists of a 6-degree blazed grating with a high groove density. The fabrication of the substrate gratings was based on scanning interference lithography and anisotropic wet etch of silicon single crystals. The optimized fabrication process provided precise control of the grating periodicity, and the grating groove profile, together with very short anti-blazed facets, and near atomically smooth surface blazed facets. The blazed grating coated with 20 Mo/Si bilayers demonstrated a diffraction efficiency in the third order as high as 33% at an incidence angle of 11° and wavelength of 14.18 nm. This work was supported by the US Department of Energy under contract number DE-AC02-05CH11231.